When a signal is sparse, a sampled signal always includes a large amount of redundant information, and the sampled signal needs to be compressed before the signal is saved and transmitted. Therefore, in 2006, persons such as Terence Tao and Donoho simultaneously came up with a concept of compressive sensing, that is, a sampling process is combined with a signal compression process, and a lowest sampling rate is directly determined, during sampling, according to a sparsity degree of a source signal, to perform sampling. Compressive sensing (compressive sensing) is a theory of performing signal reconstruction according to a sparse or compressible signal. A key to implementing compressive sensing is that a collected sample point can include as much information of a source signal as possible, that is, there is strong incoherence between a domain formed by sampling operators and a sparse domain of the signal. A lowest sampling rate determined according to the compressive sensing technology is generally lower than a Nyquist (Nyquist) rate, which greatly reduces complexity, costs, and power consumption of a sampling circuit. Especially with the constant increase in a frequency and a bandwidth of a communication signal, a conventional sampling circuit has become a vital bottleneck in the development of communications technologies, and therefore, it is particularly important to apply the compressive sensing technology to the communications field.
For a broadband analog communication signal with a sparsity feature, if sampling is directly performed by using a low-speed analog to digital converter (ADC), irreversible spectrum aliasing occurs in a signal, causing loss of information in the signal after the signal sampling. In an existing compressive sensing communications system, a structure of a random demodulator (RD) system or a modulated wideband converter (MWC) system is used, where sampling is performed after frequency mixing is first performed by using a random sequence, and then a signal is restored by using a restoration algorithm.
An existing RD system is only applicable to a signal whose frequency bins are discrete and whose frequency domain is sparse. For most communication signals having a continuous spectrum, sampling and restoration performed by using the RD system cause a relatively high restoration error, calculation complexity is very high, and a signal cannot be restored in real time. A random sequence used in the MWC system is a periodic sequence, a signal of each subband can be separately restored by using a signal restoration algorithm of the MWC system, and then complete restoration of the signal is implemented according to other related information. In an existing MWC system, because a subband bandwidth occupied by each signal is not distinguished in the system, a final sampling rate of the ADC is not determined by an actual total bandwidth of the signal but determined by a quantity of subbands occupied by the signal. Even if a bandwidth of a signal is far less than a width of a subband, because the signal occupies a subband, a sampling rate of the ADC is greatly increased. Especially because division of a subband is a fixed parameter of a system, and does not change with a signal, a frequency band boundary of the signal usually does not correspond to a subband boundary. Therefore, a signal whose frequency band width is less than a subband width spans two subbands, which causes an unnecessary increase in an ADC sampling rate.